I tend to liken Federalism to a union's collective bargining actions. Typically, Federal Nations are formed from initially independent nations' governments deciding to collectively agree to cede certain powers to a "Federal Government" while retaining other powers of a nation-state for themselves. For example, the United States ceded regulation to external commerce and foreign policy to a collective bargaining Union (The Federal Government) but not other actions, say, on zoning or land use laws. It's why a lot of federal nations tend to have capital cities in historical middles of the nation, and often times these cities are planned and much "newer" than other cities from that period (U.S., Brazil, and Australia all have capital cities that were purpose built and are not the major world cities of those nations. And there not the only federations with small planned capitals, just the ones everyone knows).
With a suzerainty, the junior nation in the relationship is more like Lando Calerissian while the senior nation is Darth Vader. If the Junior Nation doesn't agree with the Senior Nation's policy, they are more than welcome to protest, but ultimatly they'll find that the senior nation "has altered the deal" and they should pray it's not further altered. Generally, it occurs when the senior nation can power project and has interest in junior nation in so far as they can further those power projections, but not in so far as they actually care about the junior partner's existance outside of their own. The Junior Nation might enter for weapons or military hardware in exchange for the senior's own export of goods, or a small chunk of land for a forward base, and while the deal may benefit senior partner and upset the junior partner, it's a lot better than going it alone against the regional power that hates them. In the star wars example, Vader really didn't care about the small mining operation on Cloud City (or the possible loose reading of the laws and regulations of the industry) but rather, it was because Cloud City could be used to capture Luke and turn him... once that was done, they would thank the Cloud City by not caring about them... until the next time they needed them. The first film has a scene where from the discussion, the Death Star and it's status as one of the biggest sticks meant that the Emperor no longer needed the frustration that was the much more limited senate for governing planetary issues. Rather than deal with getting out of a Bacta Tank Bath for every whiny Moff or pissy senator, Palpatine could make the problem go away in a way that the whiner probably wouldn't like.
The difference is the difference between volunteering to work for a common good, and being volun-told to work for a common good.